Efforts to tie the Boston Marathon bombing to the immigration reform debate has picked up only mild momentum among members of Congress. But several lawmakers said Monday the connection should be put to rest for good.

Patrick Leahy (D-Vt.), the chairman of the Senate Judiciary Committee, publicly chastised opponents of the immigration bill who argued that the Boston attack should cause Congress to slow down the process.

"Late last week, opponents of comprehensive immigration reform began to exploit the Boston Marathon bombing," he said during a major hearing on the immigration bill. "I urge restraint in that regard."

Leahy noted that the vast majority of refugees and asylum-seekers in the U.S. make positive contributions to American society and said that the bipartisan "Gang of Eight" immigration proposal would strengthen border security and interior enforcement, which may help identify "those who would do us harm" in the future.

"Let no one be so cruel as to try to use the acts of two young men last week to derail the dreams and futures of millions of hardworking people," Leahy said.

Leahy's comments appeared to be a direct rebuke of the committee's top Republican, Sen. Chuck Grassley, who last week said that the attack in Boston "will help shed light on the weaknesses in our system."

Grassley on Monday shot back at Leahy, saying that "I did not accuse you of using the Newtown killings as an excuse," in reference to the Vermont senator arguing for stricter gun laws.

He also defended his decision to use the Boston attack as a basis to asks questions about the immigration bill.

"Once in 25 years we deal with immigration," he said, "[I want to] make sure that every base is covered."

The hearing got heated after Sen. Chuck Schumer (D-N.Y.) went after those who tried to use Boston as an "excuse" to delay consideration of the immigration bill.

"I never said that!" shouted Grassley, as he leaned across the rostrum in Schumer's direction. The New York senator said that he was not speaking about a member of the committee, but reports he read in the press.

Leahy had to gavel the committee back to order.

Meanwhile, outside the hearing room, another high-profile GOP senator joined the ranks of those tying Boston to the immigration debate. Sen. Rand Paul (Ky.), who supports legalizing undocumented immigrants, penned a letter saying that national security concerns should be incorporated into an immigration bill.

"The facts emerging in the Boston Marathon bombing have exposed a weakness in our current system," he wrote. "If we don't use this debate as an opportunity to fix flaws in our current system, flaws made even more evident last week, then we will not be doing our jobs."

Much of this talk is based on the fact that both of the alleged perpetrators of the Boston bombing were born in Kyrgyzstan and were of Chechen ethnicity, and both had lived in the U.S. legally for about a decade.

Dzhokhar Tsarnaev, 19, was a naturalized U.S. citizen. Tsarnaev's older brother and the other suspect, Tamerlan, did not have citizenship. He was reportedly questioned by the FBI in 2011 about supposed ties to radical Islam, but the agency did not find any terrorist activity at the time, according to the Associated Press.

In reality, there is no proven connection between increased immigration and the likelihood of terror plots. Terrorists such at the unabomber and the Olympic Park bomber were both American citizens. Still, Grassley said Monday that he had a litany of questions about the bill, such as the speed with which the interior enforcement mechanisms would be put into place and how effective the new border security measures would be.

"If we don't secure our borders up front, there will be no political will to try and do it later," he said.